Motion in a Plane Class 11 Notes | Projectile Motion | IIT JEE | NEET

The range of a projectile is R = u² sin2θ / g, where u is the initial speed, θ is the launch angle, and g is acceleration due to gravity (9.8 m/s²). Maximum range occurs at θ = 45°, giving R_max = u²/g. Complementary angles like 30° and 60° always produce the same range.

A scalar has only magnitude — examples include speed, mass, and temperature. A vector has both magnitude and direction — examples include velocity, displacement, and force. In Class 11, understanding this difference is essential before attempting any problem involving two-dimensional motion.

The horizontal motion of a projectile is uniform (constant velocity), while the vertical motion is uniformly accelerated (under gravity). When you combine x = ucosθ · t and y = usinθ · t − ½gt², and eliminate t, you get y = x tanθ − gx²/(2u²cos²θ) — which is the equation of a parabola.

Centripetal acceleration arises in uniform circular motion because even though speed is constant, the direction of velocity continuously changes. This change in direction requires acceleration, which always points toward the centre of the circle. Its magnitude is a = v²/r, where v is speed and r is the radius of the circular path.

Based on NTA's official JEE Main papers from 2019 to 2024, this chapter typically contributes 1 to 2 questions per paper. The most common topics tested are projectile motion (range, height, time of flight) and centripetal acceleration in uniform circular motion. Horizontal projection is another frequently appearing subtopic.